Adding fractions with like denominators worksheets | Worsheets library - Free Printable

Problem: Adding Fractions (Like Denominators)

The task involves solving a series of fraction addition problems where the denominators are the same. When adding fractions with like denominators, you simply add the numerators and keep the denominator unchanged.

Let's solve each problem step by step:

---

Problem 1:

$$
\frac{3}{4} + \frac{3}{4}
$$
- Add the numerators: \(3 + 3 = 6\)
- Keep the denominator: \(4\)
- Result: \(\frac{6}{4}\)
- Simplify: \(\frac{6}{4} = \frac{3}{2}\) (divide numerator and denominator by 2)

Answer: \(\frac{3}{2}\)

---

Problem 2:

$$
\frac{5}{7} + \frac{6}{7}
$$
- Add the numerators: \(5 + 6 = 11\)
- Keep the denominator: \(7\)
- Result: \(\frac{11}{7}\)

Answer: \(\frac{11}{7}\)

---

Problem 3:

$$
\frac{16}{25} + \frac{12}{25}
$$
- Add the numerators: \(16 + 12 = 28\)
- Keep the denominator: \(25\)
- Result: \(\frac{28}{25}\)

Answer: \(\frac{28}{25}\)

---

Problem 4:

$$
\frac{23}{100} + \frac{54}{100}
$$
- Add the numerators: \(23 + 54 = 77\)
- Keep the denominator: \(100\)
- Result: \(\frac{77}{100}\)

Answer: \(\frac{77}{100}\)

---

Problem 5:

$$
\frac{6}{9} + \frac{1}{9}
$$
- Add the numerators: \(6 + 1 = 7\)
- Keep the denominator: \(9\)
- Result: \(\frac{7}{9}\)

Answer: \(\frac{7}{9}\)

---

Problem 6:

$$
\frac{8}{10} + \frac{4}{10}
$$
- Add the numerators: \(8 + 4 = 12\)
- Keep the denominator: \(10\)
- Result: \(\frac{12}{10}\)
- Simplify: \(\frac{12}{10} = \frac{6}{5}\) (divide numerator and denominator by 2)

Answer: \(\frac{6}{5}\)

---

Problem 7:

$$
\frac{4}{6} + \frac{4}{6}
$$
- Add the numerators: \(4 + 4 = 8\)
- Keep the denominator: \(6\)
- Result: \(\frac{8}{6}\)
- Simplify: \(\frac{8}{6} = \frac{4}{3}\) (divide numerator and denominator by 2)

Answer: \(\frac{4}{3}\)

---

Problem 8:

$$
\frac{18}{50} + \frac{42}{50}
$$
- Add the numerators: \(18 + 42 = 60\)
- Keep the denominator: \(50\)
- Result: \(\frac{60}{50}\)
- Simplify: \(\frac{60}{50} = \frac{6}{5}\) (divide numerator and denominator by 10)

Answer: \(\frac{6}{5}\)

---

Problem 9:

$$
\frac{13}{20} + \frac{11}{20}
$$
- Add the numerators: \(13 + 11 = 24\)
- Keep the denominator: \(20\)
- Result: \(\frac{24}{20}\)
- Simplify: \(\frac{24}{20} = \frac{6}{5}\) (divide numerator and denominator by 4)

Answer: \(\frac{6}{5}\)

---

Problem 10:

$$
\frac{7}{11} + \frac{7}{11}
$$
- Add the numerators: \(7 + 7 = 14\)
- Keep the denominator: \(11\)
- Result: \(\frac{14}{11}\)

Answer: \(\frac{14}{11}\)

---

Problem 11:

$$
\frac{15}{25} + \frac{7}{25}
$$
- Add the numerators: \(15 + 7 = 22\)
- Keep the denominator: \(25\)
- Result: \(\frac{22}{25}\)

Answer: \(\frac{22}{25}\)

---

Problem 12:

$$
\frac{4}{7} + \frac{3}{7}
$$
- Add the numerators: \(4 + 3 = 7\)
- Keep the denominator: \(7\)
- Result: \(\frac{7}{7} = 1\)

Answer: \(1\)

---

Problem 13:

$$
\frac{1}{3} + \frac{1}{3}
$$
- Add the numerators: \(1 + 1 = 2\)
- Keep the denominator: \(3\)
- Result: \(\frac{2}{3}\)

Answer: \(\frac{2}{3}\)

---

Problem 14:

$$
\frac{4}{8} + \frac{3}{8}
$$
- Add the numerators: \(4 + 3 = 7\)
- Keep the denominator: \(8\)
- Result: \(\frac{7}{8}\)

Answer: \(\frac{7}{8}\)

---

Problem 15:

$$
\frac{2}{5} + \frac{2}{5}
$$
- Add the numerators: \(2 + 2 = 4\)
- Keep the denominator: \(5\)
- Result: \(\frac{4}{5}\)

Answer: \(\frac{4}{5}\)

---

Problem 16:

$$
\frac{8}{16} + \frac{10}{16}
$$
- Add the numerators: \(8 + 10 = 18\)
- Keep the denominator: \(16\)
- Result: \(\frac{18}{16}\)
- Simplify: \(\frac{18}{16} = \frac{9}{8}\) (divide numerator and denominator by 2)

Answer: \(\frac{9}{8}\)

---

Problem 17:

$$
\frac{3}{12} + \frac{6}{12}
$$
- Add the numerators: \(3 + 6 = 9\)
- Keep the denominator: \(12\)
- Result: \(\frac{9}{12}\)
- Simplify: \(\frac{9}{12} = \frac{3}{4}\) (divide numerator and denominator by 3)

Answer: \(\frac{3}{4}\)

---

Problem 18:

$$
\frac{1}{2} + \frac{1}{2}
$$
- Add the numerators: \(1 + 1 = 2\)
- Keep the denominator: \(2\)
- Result: \(\frac{2}{2} = 1\)

Answer: \(1\)

---

Problem 19:

$$
\frac{3}{13} + \frac{7}{13}
$$
- Add the numerators: \(3 + 7 = 10\)
- Keep the denominator: \(13\)
- Result: \(\frac{10}{13}\)

Answer: \(\frac{10}{13}\)

---

Problem 20:

$$
\frac{8}{15} + \frac{11}{15}
$$
- Add the numerators: \(8 + 11 = 19\)
- Keep the denominator: \(15\)
- Result: \(\frac{19}{15}\)

Answer: \(\frac{19}{15}\)

---

Problem 21:

$$
\frac{3}{14} + \frac{4}{14}
$$
- Add the numerators: \(3 + 4 = 7\)
- Keep the denominator: \(14\)
- Result: \(\frac{7}{14}\)
- Simplify: \(\frac{7}{14} = \frac{1}{2}\) (divide numerator and denominator by 7)

Answer: \(\frac{1}{2}\)

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Final Answers:

1. \(\frac{3}{2}\)
2. \(\frac{11}{7}\)
3. \(\frac{28}{25}\)
4. \(\frac{77}{100}\)
5. \(\frac{7}{9}\)
6. \(\frac{6}{5}\)
7. \(\frac{4}{3}\)
8. \(\frac{6}{5}\)
9. \(\frac{6}{5}\)
10. \(\frac{14}{11}\)
11. \(\frac{22}{25}\)
12. \(1\)
13. \(\frac{2}{3}\)
14. \(\frac{7}{8}\)
15. \(\frac{4}{5}\)
16. \(\frac{9}{8}\)
17. \(\frac{3}{4}\)
18. \(1\)
19. \(\frac{10}{13}\)
20. \(\frac{19}{15}\)
21. \(\frac{1}{2}\)

Boxed Final Answer:
\[
\boxed{
\begin{array}{lll}
1. & \frac{3}{2} & 2. & \frac{11}{7} & 3. & \frac{28}{25} \\
4. & \frac{77}{100} & 5. & \frac{7}{9} & 6. & \frac{6}{5} \\
7. & \frac{4}{3} & 8. & \frac{6}{5} & 9. & \frac{6}{5} \\
10. & \frac{14}{11} & 11. & \frac{22}{25} & 12. & 1 \\
13. & \frac{2}{3} & 14. & \frac{7}{8} & 15. & \frac{4}{5} \\
16. & \frac{9}{8} & 17. & \frac{3}{4} & 18. & 1 \\
19. & \frac{10}{13} & 20. & \frac{19}{15} & 21. & \frac{1}{2} \\
\end{array}
}
\]